Automorphisms of unitary block designs
Automorphisms of unitary block designs
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DOI：
10.1016/0021-8693(72)90070-1
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发表时间：
1972-03
影响因子：
0.9
通讯作者：
Michael E. O'Nak
中科院分区：
文献类型：
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作者：
Michael E. O'Nak
本文讨论了与三维酉群相关的酉或酉块设计的几何性质，并确定了它们的自同构群。如果V是具有q2个元素的场上的三维向量空间，b是V上的非简并厄米双线性形式，则设X表示V关于b的各向同性一维子空间族。则X有1+ q3个点，并且三维射影酉群PSU （3, q）和PGU （3, q）作为双传递置换群作用于X。X， d有一个自然产生的子集族，在X上形成一个酉块设计。d中的每个元素是v的一个固定的非各向同性二维子空间中包含的各向同性一维子空间的集合。我们的主要结果是：
In this paper, we discuss the geometry and determine the automorphism group of the unital or unitary block design associated with the threedimensional unitary group.If V is a three-dimensional vector space over the field with q2 elements and b is a non degenerate Hermitian bilinear form on V, we let X denote the family of isotropic one-dimensional subs paces of V with respect to b. Then X has 1+ q3 points, and the three-dimensional projective unitary groups, PSU (3, q) and PGU (3, q), act on X as doubly-transitive permutation groups. There is a naturally arising family of subsets of X, d, forming a unitary block design on X. Each member of d is the set of isotropic one-dimensional subs paces contained in a fixed nonisotropic two-dimensional subspace of V. Our principal result is: